A heuristic for large-sizep-median location problems with application to school location

Abstract

This paper initially proposes a heuristic algorithm for thep-median problem designed for large weighted graphs. The problem is approached through the construction ofp trees whose shapes are progressively modified according to successive tests over the stability of their roots and vertices. The algorithm seems promising because: (i) on a regular PC it can handle problems of the order of 500 vertices, while the mainframe version goes indefinitely further, (ii) contrary to what normally would be expected, execution times seem to be inversely proportional top, and even for large problems, they may be reasonable, especially ifp is large relative to the number of vertices, and (iii) it produces solutions of good quality and in most of the cases studied, it outperforms the traditional heuristic of Teitz and Bart. A real application of the algorithm embedded in a methodology to evaluate the location of 85 public schools, among 389 possible vertices, in the metropolitan area of Rio de Janeiro is reported. Results confirmed the conjecture of poor location and the procedure was able to identify several micro-regions simply void of schools. The methodology is being well received by the education authorities and its extension to the whole metropolitan area is being considered.